Without having to watch the video, I am freaking out when a spellcaster tries something like that either.
The problem is really not the power. The problem is that spellcasters usually get their power much faster.
Really? Shall I break that down for you then?
First part of the video: The Javelins.
I see somewhere around 25 javelins in this guy. Because they where all rather the size of spears we wills ay they are large javelins (same bloody thing) which is would make it 25d8 = 112 base damage on average. The character seems quite unfazed by the damage, possible from damage reduction or perhaps a bit of fast healing.
Second part of the video: The random mooks.
There are a bunch of one-shotted mooks, that indicate no real power level of their own. With Cleave, that's about one or two rounds worth of attacks, if the barbarian has Pounce. He has some sort of AoE knockout move, which seems rather similar to a fireball in range of fierceness.
Interlude of the video: Dude was hit by a huge greatsword, which doesn't do damage. Damage reduction or even natural AC takes the hit.
Third part of the Video: The marble column that he lifts and swings about hits pretty damn hard. He manages to carry and run at something with a bloody marble column. Without some kind of feat/feature, this is the most demanding part of the entire video, because running requires you to be under no more than a medium load at best, and that thing is fairly big/heavy. He also seems to do good unarmed damage.
The finale of the video: Finale (Sue me)
The guy is fighting another in fisticuffs, no big deal at all. The giant finger that is cast shows us no mechanics that are superior to crushing fist of spite, which does a max of 20d6 with a reflex save for half damage. Dude is pretty much incapacitated from it with one hit. Can't say if he did or did not make his save, though it seemed like it was a fort save and he made it from my eyes due to the glorified representation of the aftermath. So he took another 20d6/2=35 or so damage. After which he is done.
This is at most level 8-12 territory, the thing is that it's a barbarian doing this instead of a wizard. But while this guy does it with DR, a wizard could all the same feats in the movie at level 10 - if that video clip is a 'same game test' a level 10 wizard can do it fine, and no one would even think twice about it because he is a wizard.
D&D spellcasters are anything and everything. He is a fireball tosser who also happens to conjures illusionary walls, and a guy who turns invisible and summons monsters to kill everything. He is able to blind and stun enemies with battlefield control, translate any language, teleport and turn his self into a wartroll or dragon to fight people.
That's all the stuff that a wizard can do, and does do all the time.
What we have is people saying that it's wrong for the fighter class to be both a heavily armored full plate tank and a mobile swashbuckler type or anything else. The wizard can get away with being seriously everything. Yet handing out proficiency in every martial weapon to the fighter some how gets the realism police out there. Because as a fighter you have to fit in this super small square of what you can or can not do. People are not even content to just say you can't do magic. No, you have to wear a specific type of armor and you have to even specialize in a specific weapon that you will use for the rest of your characters life. You can forget about being a swordsman and an archer, you're lucky if you end up being competent using a longsword and a warhammer. And that's before you start finding magic weapons that further pigeonhole you into more limitations.
That's similar to if we took the wizard class and forced him to choose a single spell that he would be able to cast, and told them, This is all you can cast. Maybe you learn little variations on it or make the spell a bit stronger, but you never learn anything else. Ever regardless of what happens.
Just imagine that for a bit. You never get to learn any other gimmicks other than that one signature spell. Wizard players would be up in arms and furious. And yet this is what the fighter has had to live with since day one.
The fighter really needs to break out of his box. I don't know why the fighter shouldn't be able to be both a lightly armored warrior and a heavily armored warrior, you seriously don't even have to make him choose. He could get abilities for both and depending on if he's strength based or dex based, you go from there. Rogue and fighter are basically the same concept and there is no problem with simply giving the rogue's "out of combat skill abilities" to the fighter. This would help somewhat, but leave the other classes out to dry (specifically the rouge).
What really needs to be done is to simply start ignoring the little boxes that classes are put in and give them the abilities, but just use fluff to explain it. Let the fighter have teleport 100 ft., let the rouge be able to turn invisible, let the barbarian be able to enlarge person himself, you get the idea.
When you have a class that doesn't require magic items to do any of these things, and only uses magic items to further increase his already vast power gap from other classes you really need to sit down and fix it. Especially when all those magic items that the other classes require to be able to do squat are produced by the ones that are already with out them so much more powerful than the ones that don't.
Edit: Damn, I'm ranting again, sorry!
But don't expect them to alllll go the distance. 
